I board at NYP heading SB all the time before anyone else gets on. About 10% of the seats are taken by through travelers, the rest are empty. Most people get on or off in NY, and the trains run through more for operational efficiency than anything else.
Amtrak doesn't make it "as hard as possible," they want families on their trains, as you're still a paying customer. The operational realities of New York Penn, primarily the narrow platforms, require this, and assigned seating isn't going to happen with coach seats for a variety of reasons. If you want assigned seating, buy business class, though the same problem will occur if you don't book far enough out as they won't save any seat pairs for you.
If you look at their website they have lots of information on ways to make things easier, including the easiest solution - getting a Red Cap to take you down to the train before everyone else gets on. You SHOULD tip but you do not HAVE to tip. Or, a little secret the frequent passengers know: when you hear the track number announced, you can dash down through the Long Island railroad concourse and get on the train before the escalator's been opened, though if you have lots of luggage this may not be a good solution.
Worst case scenario, you will be able to find some seats close to each other, and if it's such a sold out train that you can't find some aisle seats across from each other, someone will be willing to move to help you out, but you will have to seek that person out. Once someone is sat in their seat, they are under no obligation to relinquish it for your convenience, and many won't, as it may mean they have to sit next to someone when they otherwise wouldn't have to.
If you say something nasty to a commuter for doing what they’re allowed to do, expect them to come back swinging, and pray that’s only in the metaphorical sense.
TLDR: Get a red cap, it's worth the 5 bucks and you're saving a hell of a lot more than that on the steeply discounted child rate.